Hypothesis Test Problem

Hello,

I have a problem involving making a Hypothesis Test for a treatment being performed. The outcome is measured with a health rating FIM. There are 203 patients before treatment and 203 after treatment , each has a health measurement FIM. I found a sample mean of 41.8 before treatment with a variance of 58.5, and a sample mean of 61.5 after treatment with a variance of 99.7. I want to perform hypothesis testing on this. I made the null hypothesis that the average after the treatment was the same as the sample mean before the treatment (41.8). Was that wrong to do?

When finding the z-score of the result I got approx. 28, which I do not think is correct because of how high it is. From what I understand I have too many samples for a two sample t-test correct? But nonetheless when I perform that I get a score of approx. 22. Which I think may also be incorrect.

Re: Hypothesis Test Problem

(standard deviation of FIM at discharge)/sqrt(total number of patients) = 0.7006

(mean of FIM at discharge - mean of FIM at admission) = 19.6108

19.6018/0.7006 = 28

For the t-test I used:
t = (mean of FIM at admission - mean of FIM at discharge)/ sqrt((SD1^2/203 + SD2^2/203))

(41.8 - 61.5)/ 0.883 = -22.2

The patients at discharge are the same patients at admission, so there should be a strong relationship.
I think I may understand what the problem is, I need to be calculating the mean differences between the tests. Is that correct?